Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.

doi:10.2514/1.J053838

Title: Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Abstract

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model,more »« less

Authors:

Kuether, Robert J. ^[1]; Deaner, Brandon J. ^[2]; Hollkamp, Joseph J. ^[3]; Allen, Matthew S. ^[1]

Univ. of Wisconsin, Madison, WI (United States)
Mercury Marine, Fond du Lac, WI (United States)
U.S. Air Force Research Lab., Wright-Patterson Air Force Base, OH (United States)

Publication Date:: Tue Sep 15 00:00:00 EDT 2015

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: Air Force Office of Scientific Research, OH (United States)

OSTI Identifier:: 1237462

Report Number(s):: SAND-2015-2368J
Journal ID: ISSN 0001-1452; 579511

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: AIAA Journal

Additional Journal Information:: Journal Volume: 53; Journal Issue: 11; Journal ID: ISSN 0001-1452

Publisher:: AIAA

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Kuether, Robert J., Deaner, Brandon J., Hollkamp, Joseph J., and Allen, Matthew S. Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes.  United States: N. p., 2015. 
Web.  doi:10.2514/1.J053838.

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                    Kuether, Robert J., Deaner, Brandon J., Hollkamp, Joseph J., & Allen, Matthew S. Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes.  United States.  https://doi.org/10.2514/1.J053838

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                    Kuether, Robert J., Deaner, Brandon J., Hollkamp, Joseph J., and Allen, Matthew S. Tue .  
"Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes".  United States.  https://doi.org/10.2514/1.J053838.  https://www.osti.gov/servlets/purl/1237462.

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@article{osti_1237462,

  title        = {Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes},

  author       = {Kuether, Robert J. and Deaner, Brandon J. and Hollkamp, Joseph J. and Allen, Matthew S.},

  abstractNote = {Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.},

  doi          = {10.2514/1.J053838},

  journal      = {AIAA Journal},

  number       = 11,

  volume       = 53,

  place        = {United States},

  year         = {Tue Sep 15 00:00:00 EDT 2015},

  month        = {Tue Sep 15 00:00:00 EDT 2015}

}

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Works referenced in this record:

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Title: Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Abstract

Citation Formats

Reduced-Order Models for Acoustic Response Prediction of a Curved Panel conference, June 2012

Verification Studies on Hypersonic Structure Thermal/Acoustic Response and Life Prediction Methods conference, April 2013

Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques journal, January 2009

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Normal Modes of Nonlinear Dual-Mode Systems journal, June 1960

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW journal, January 1997

Nonlinear normal modes, Part I: A useful framework for the structural dynamicist journal, January 2009

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes journal, January 2011

Nonlinear modal models for sonic fatigue response prediction: a comparison of methods journal, June 2005

A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures journal, May 2013

A Finite Element time Domain Modal Formulation for Large Amplitude free Vibrations of Beams and Plates journal, June 1996

Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells journal, October 2011

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation journal, July 1996

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 2: Example Calculations journal, July 1996

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A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Non-Linear beam to Harmonic Excitation journal, June 2001

Reduced-order models for nonlinear response prediction: Implicit condensation and expansion journal, December 2008

Alternative modal basis selection procedures for reduced-order nonlinear random response simulation journal, August 2012

System identification-guided basis selection for reduced-order nonlinear response analysis journal, August 2008

Relationships between Nonlinear Normal Modes and Response to Random Inputs conference, January 2014

Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment journal, May 2005

The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation conference, June 2012

Reduced-Order Modeling of Random Response of Curved Beams Using Implicit Condensation conference, June 2012

On the Use of Reduced-Order Models for a Shallow Curved Beam Under Combined Loading conference, June 2012

Relationships between nonlinear normal modes and response to random inputs journal, February 2017

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Identifying the significance of nonlinear normal modes journal, March 2017

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Verification Studies on Hypersonic Structure Thermal/Acoustic Response and Life Prediction Methods
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Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques
journal, January 2009

A numerical approach to directly compute nonlinear normal modes of geometrically nonlinear finite element models
journal, May 2014

Normal Modes of Nonlinear Dual-Mode Systems
journal, June 1960

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW
journal, January 1997

Nonlinear normal modes, Part I: A useful framework for the structural dynamicist
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Dynamic testing of nonlinear vibrating structures using nonlinear normal modes
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Nonlinear modal models for sonic fatigue response prediction: a comparison of methods
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A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures
journal, May 2013

A Finite Element time Domain Modal Formulation for Large Amplitude free Vibrations of Beams and Plates
journal, June 1996

Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells
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A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation
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Determination of nonlinear stiffness with application to random vibration of geometrically nonlinear structures
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